250 Prof. E. Taylor Jones on a 



n these measurements one storage-cell was nsed and the 

 galvanometer was shunted. Thus all the capacities were 

 measured for about 48*8 charges and discharges per second. 



(8) Formulce for calculating Periods of Oscillation. 



When the coil A alone was used the period was calculated 

 from Kelvin's formula 



• • • • (1) 



/ i jv' 



V LA 4L X 2 



in which Cx was taken as the capacity of the leyden-jar -f 



n — 2 1 



capacity of the electrometer H ^ C + tsC". 



The resistance R 1 of the coil was about 14,000 ohms, and 

 this affected the period by nearly one-fifth per cent, with 

 the largest condenser, and by only 1 in 3000 with the 

 smallest. 



When the coil B was inserted in A and its terminals left 

 disconnected, the same formula (1) was nsed to calculate the 

 period, the value of C" for these circumstances being used 

 in Ci. The influence of the brass tube on which B is \\ound 

 is discussed in the next section. 



With the terminals of B connected together it can be 

 shown that, neglecting the resistance of B and neglecting 

 the brass tube altogether, the period is given by 



T - V 1 L I (1-M 12 2 /L 1 L 3 ) 4V(1 - M^V ' w 



where L 2 is the self-inductance of B and M ]2 the mutual 

 inductance of A and B ; i. <?., it is the same as with a single 

 coil of self -inductance L x (l — M 12 2 /LiL 2 ). When the ter- 

 minals of B are connected to a condenser of capacity C 2 , each 

 coil has two periods of oscillation given by 



g?L 2 - 1 ri- + -i- + A /H 1 Y ■ 4M »' T r*i 



T2 ~ i_ ^i£ Ll i°i l A ± V iLA - LfiJ + L^L/CxCj * (3) 

 LiL 2 



Here the brass tube and all the resistances are neglected. 

 The longer wave only is usually observed and the negative 

 sign taken in calculating the period. 



* Oberbeck, Wied. Ann. lv. p. 623 (1895). 



